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Donald Trump Jr. was emailed about meeting with a Russian lawyer during last year's campaign

The oldest son of the President released a screenshot Tuesday apparently of those messages

(CNN)Hillary Clinton's former running mate, Sen. Tim Kaine, said Donald Trump Jr. may have committed treason when he agreed to meet with a Russian lawyer under the pretense of getting dirt on Clinton.

"That, the investigation -- it, it's not -- nothing is proven yet. But, we're now beyond obstruction of justice in terms of what's being investigated," the Virginia Democrat told CNN Tuesday. "This is moving into perjury, false statements and even potentially treason."

Kaine's comments follow a series of New York Times reports including one story Monday on an email sent to Trump Jr. last year stating that a Russian lawyer had "compromising" information about Hillary Clinton as "part of a Russian government effort" to help the Trump campaign. President Donald Trump's oldest son tweeted Tuesday screenshots of an email exchange that he says are the emails setting up the meeting with the lawyer. That tweet came after Kaine's comment.

A Kaine spokesperson later sent a statement to CNN saying that the matter of treason will be up to investigators to prove.

"Senator Kaine stressed that nothing is proven yet," the Kaine spokesperson said. "But he acknowledged the grave impropriety, if proven, of any effort to cooperate with a foreign nation -- especially one deemed by our military leaders to be a primary state adversary -- to influence an American election."

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Sen. John Cornyn, a high-ranking Texas Republican on the committee, said of Trump Jr.'s comments, "I don't think we have enough information to reach a conclusion but he certainly made himself a witness."

Members of the Senate intelligence committee, which is investigating possible ties between the Trump campaign and Russia, said Monday they plan to invite Trump Jr. to testify. He tweeted that he would gladly speak with investigators.

Committee chairman Richard Burr of North Carolina would not comment on Trump Jr.'s tweet, besides telling reporters that he wanted to fully vet the meeting with the Russian lawyer and that his committee is "very early in the investigation."

Sen. Lindsey Graham, a South Carolina Republican, said any time you're in a campaign and you get an offer from a foreign government the answer is "no."

"I think the transparency is the proper thing to do and I think he's shown that he wants everybody to know what the situation is, as I have found them on so many stories since the election," Grassley told CNN.

Sen. Orrin Hatch of Utah described Trump Jr. as "a very bright young man," but not a member of his father's administration. He responded to Kaine's accusations of treason with, "You got to be kidding."

"He's not in the administration," Hatch said. "He may be the son of the president but he doesn't have the authority to speak for the president. Look, I think this is overblown."

Trump Jr. has not yet testified under oath on his connections with Russian. His attorney has dismissed the revelations as "much ado about nothing" and Trump Jr. said in a statement Tuesday morning that he thought the information being offered was "Political Opposition Research."

"I first wanted to just have a phone call but when that didn't work out, they said the woman would be in New York and asked if I would meet. I decided to take the meeting. The woman, as she has said publicly, was not a government official," Trump Jr. said in a statement he tweeted along with the emails. "And, as we have said, she had no information to provide and wanted to talk about adoption policy and the Magnitsky Act."